HW_1.pdf
-
Upload
fawzi51119637872830 -
Category
Documents
-
view
212 -
download
0
Transcript of HW_1.pdf
-
Statistical Methods for Reliability Engineering Homework #1
Orlando J. Rivera-Anglero
Exercise 1
a.
b.
c.
d. Starting Cycle
Ending Cycle
f z
0 0
0 20 0.002273 0.002381
20 40 0.004545 0.005263
40 60 0.018182 0.036364
60 80 0.006818 0.01875
80 100 0.006818 0.03
100 120 0.004545 0.033333
120 140 0.004545 0.1
140 160 0.002273
Starting Cycle
Ending Cycle
# Survivors
0 0 22
0 20 21
20 40 19
40 60 11
60 80 8
80 100 5
100 120 3
120 140 1
140 160 0
Starting Cycle
Ending Cycle
R
0 0 1
0 20 0.954545
20 40 0.863636
40 60 0.5
60 80 0.363636
80 100 0.227273
100 120 0.136364
120 140 0.045455
140 160 0
Starting Cycle
Ending Cycle
F
0 0 0
0 20 0.045455
20 40 0.136364
40 60 0.5
60 80 0.636364
80 100 0.772727
100 120 0.863636
120 140 0.954545
140 160 1
-
Statistical Methods for Reliability Engineering Homework #1
Orlando J. Rivera-Anglero
e. >
>
Exercise 2
Based on the chart above and the correlation coefficient, it is determined that a Weibull
distribution provides the best fit for the data.
10010
90
50
10
1
St Cycle
Percent
10010
99
90
50
10
1
St Cycle
Percent
100101
90
50
10
1
St Cycle
Percent
10010
99
90
50
10
1
St Cycle
Percent
Weibull
0.991
Lognormal
0.983
Exponential
*
Loglogistic
0.983
C orrelation C oefficient
Probability Plot for St CycleLSXY Estimates-Arbitrary Censoring
Weibull Lognormal
Exponential Loglogistic
150100500
0.012
0.008
0.004
0.000
St Cycle
PDF
10010
90
50
10
1
St Cycle
Percent
150100500
100
50
0
St Cycle
Percent
150100500
0.06
0.04
0.02
0.00
St Cycle
Rate
Shape 2.22947
Scale 82.6234
Mean 73.1777
StDev 34.6962
Median 70.0983
IQR 48.4096
AD* 0.703
C orrelation 0.991
Table of StatisticsProbability Density Function
Surv iv al Function Hazard F unction
Distribution Overview Plot for St CycleLSXY Estimates-Arbitrary Censoring
Weibull
-
Statistical Methods for Reliability Engineering Homework #1
Orlando J. Rivera-Anglero
Then a Distribution Overview Plot is created to find the missing parameters of the
Weibull distribution equation. It is found the scale = 82.6234 and the shape = 2.22947.
Now we can go into Maple and substitute these values into the equation.
>
>
>
>
>
>
>
>
-
Statistical Methods for Reliability Engineering Homework #1
Orlando J. Rivera-Anglero
>
-
Statistical Methods for Reliability Engineering Homework #1
Orlando J. Rivera-Anglero
>
-
Statistical Methods for Reliability Engineering Homework #1
Orlando J. Rivera-Anglero
Exercise 3 Refer to Excel file HW1_E3.xls for Monte Carlo simulation results.
150100500
0.012
0.008
0.004
0.000
t
PDF
100101
99.99
90
50
10
1
0.01
t
Percent
150100500
100
50
0
t
Percent
150100500
0.06
0.04
0.02
0.00
t
Rate
C orrelation 0.999
Shape 2.21863
Scale 81.0299
Mean 71.7645
StDev 34.1753
Median 68.6911
IQ R 47.6695
Failure 1000
C ensor 0
AD* 0.456
Table of StatisticsProbability Density F unction
Surv iv al F unction Hazard F unction
Distribution Overview Plot for tLSXY Estimates-Complete Data
Weibull
-
Statistical Methods for Reliability Engineering Homework #1
Orlando J. Rivera-Anglero
When we compare the results obtained from the Excel spread sheet versus the results
obtained from Minitab, it can be seen that the MEAN value is very similar.
Exercise 4
See Maple file HW1_E4.mw for results.
Exercise 5
>
>
>
>
>
>
>
>
>
>
>
>
-
Statistical Methods for Reliability Engineering Homework #1
Orlando J. Rivera-Anglero
>